3. A potassium ion channel in a cell membrane is filled with intracellular fluid

Question

3. A potassium ion channel in a cell membrane is filled with intracellular fluid. Ions of chargee flow through the channel at a rate of 1.0x10 ions/second. The potential difference across the channel is 70mV. The channel has the shape of a cylinder with a diameter of 0.30nm and a length of 5.0nm. Calculate... a) the current through the channel. b) the resistance of the ion channel. c.. the resistivity of the intracellular fluid. d)... the electric field in the channel. d)... the power dissipated in the channel.

Explanation / Answer

3. (A) I = Q/ t = (1 x 10^7)(1.6 x 10^-19) C / s

I = 1.6 x 10^-12 A

(B) R = V / I = (70 x 10^-3) / I = 4.375 x 10^10 ohm

(C) R = rho L / A

4.375 x 10^10 = rho (5 x 10^-9) / (pi (0.30 x 10^-9/2))

rho = 0.6185 ohm m

(D) E = V / L = 0.070 / (5 x 10^-9)

E = 14 x 10^6 V/m

(E) P = VI = 1.12 x 10^-13 Watt

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